Positional control system for a machine tool

ABSTRACT

This invention relates to a vector measurement system for controlling positional movement of a machine tool spindle along two mutually perpendicular axes respectively perpendicular to the axis of spindle rotation. The spindle is journaled in a spindlehead vertically movable on a column that is horizontally movable on a supporting base. Separate power translators are respectively connected to effect horizontal column movement and vertical spindlehead movement in accordance with separate feedback error control signals. A pair of separate lineal measuring instruments which are pivotally secured at one end to the spindle, extend in angularly diverging directions and are pivotally secured at their opposite outer ends to spaced apart portions of the support base. A positional control system responsive to vector measurements from both diagonally disposed, pivotally interconnected lineal measuring transducers provides separate feedback error control signals for indicating the spindle position along its respective horizontal and vertical axes. Predetermined digital input command signals actuate the separate power translators for moving the tool spindle horizontally and vertically to a position determined by positional error feedback signals from the vector measurement control system. In a similar manner, error feedback signals from the vector measurement control system operate to control bodily movement of the tool spindle along only one axis of movement. During each single axis movement, rectilinear positional measurement signals from both pivotally interconnected vector measuring transducers are connected to provide orthogonal positional error control signals.

United States Patent [72] Inventors WlllaeeEBralnard New Berlin; EdwardE. Klrklmm, Brookfield, both of, Wis. [2| Appl. No. 755,206 [22] FiledAug. 26,1968 {45] Patented July 27, 1971 [73] Assignee Kearney & TreckerCorporation West Allis, Wis.

[54] POSITIONAL CONTROL SYSTEM FOR A MACHINE TOOL 16 Claims, 9 DrawingFigs. 52 us. Cl .1 318/574, 318/640, 235/151.n [s11 Int.Cl G05b 19/100[50] FleldolSearch "ms/151.11; sums-33 [56] References Cited UNITEDSTATES PATENTS 3,206,857 9/1965 Kaye ..23s/1s1.n ux

Primary ExaminerBenjamin Dobeck Attorneys-Donald E. Porter and WilliamC. Gleisner, .lr.

ABSTRACT: This invention relates to a vector measurement system forcontrolling positional movement of a machine tool spindle along twomutually perpendicular axes respectively perpendicular to the axis ofspindle rotation. The spindle is joumaled in a spindlehead verticallymovable on a column that is horizontally movable on a supporting base.Separate power translators are respectively connected to effecthorizontal column movement and vertical spindlehead movement inaccordance with separate feedback error control signals. A pair ofseparate lineal measuring instruments which are pivotally secured at oneend to the spindle, extend in angularly diverging directions and arepivotally secured at their opposite outer ends to spaced apart portionsof the support base. A positional control system responsive to vectormeasurements from both diagonally disposed, pivotally interconnectedlineal measuring transducers provides separate feedback error controlsignals for indicating the spindle position along its respectivehorizontal and vertical axes. Predetermined digital input commandsignals actuate the separate power translators for moving the toolspindle horizontally and vertically to a position determined bypositional error feedback signals from the vector measurement controlsystem. In a similar manner,

error feedback signals from the vector measurement control systemoperate to control bodily movement of the tool spindle along only oneaxis of movement. During each single axis movement, rectilinearpositional measurement signals from both pivotally interconnected vectormeasuring transducers are connected to provide orthogonal positionalerror control signals.

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SHEET 3 BF 9 /SPINDLEAXIS 82 H PIVOT AXIS F ICT 5 v la INVENTOR5 WALLACEE. RA/NARD 65 EDWARD E. lR/(HAM ATTOQNEY PATENTED JUL2 7 Ian SHEET 8 BF9 YAXIS lsT POSITION 2ND POSITION SPINDLE Axls AXIS H PIVOT AXIS //v v/vTORS VAL LACE EBRA/A/ARD EDWARD E/(AQ/(HAM A TTORNE V PATENTED JuLzmnsum 8 0F 9 POSITIONAL CONTROL SYSTEM FOR A MACHINE TOOL BACKGROUND OFTHE INVENTION In prior machine tools and control systems thereforseparate rectilinear transducers are adapted to control orthogonalmovements along axes in fixed parallelism to the respective transducers.For example, a rectilinear transducer scale horizontally affixed to asupport base is disposed to cooperate with an electrical positioningreading head secured to a column horizontally movable along the base.Thus, the horizontal transducer directly provides a positional feedbackerror signal for controlling horizontal movement of the column and atool spindle carried thereby along the base. In a similar manner, arectilinear transducer scale vertically affixed to the column coactswith a cooperating reading head secured to a spindlehead verticallymovable along the column and above the base. Consequently, the verticaltransducer directly provides a vertical positional feedback errorcontrol signal for controlling positional movement of the spindleheadand a tool spindle carried thereby vertically along the column andrelative to a workpiece carried by the base. Thus, the tool spindle inprior machines is journaled in the spindlehead in a fixed,laterallyspaced relationship to the vertical readinghead carried therebyand in a variable, vertically spaced relationship above the horizontalreading head secured to the lower portion of the column adjacent thesupport base. Since both the horizontal and vertical position measuringtransducers are thus remote from the position of the spindle beingcontrolled, any errors in the cooperating spindlehead, column, and baseslides contribute to errors in the selected position of the spindle.With the tool spindle positioned 30 inches vertically above the base,for example, horizontal positional measurements of the spindle would bedetermined by the horizontal transducer at-a distance of 30 inches fromthe spindle. In such a case, it will be readily apparent thatpositioning movement of the spindle along a horizontal axis iscompletely dependent upon the accuracy of a positioning transducer thatis remote from the spindle by a distance of 30 inches. Thus, anydeparture from true straight line motion in the cooperating slidesbetween the base and the column due to ways that are not straight,nonparallel or skewed will directly result in errors in the selectedhorizontal positioning movement of the tool spindle. In prior machines,similar deviations in straight line motion between the spindlehead andvertical column likewise result in errors in positioning movement of thespindle in a vertical direction.

SUMMARY OF THE INVENTION According to this invention, a pairofrespectively extensible laser interferometers are arranged'to comprisetriangulation means for measuring and controlling positional movement ofa machine member along orthogonal axes and relative to spaced apartportions of the machine frame. The triangulation measuring means areincorporated in a machine tool comprising essentially a support base, acolumn horizontally movable along the base, a spindlehead verticallymovable along the column, and a horizontal tool spindle journaled in thespindlehead. A pair of servo-controlled power translators arerespectively connected to effect servo-controlled power driven movementof the column horizontally along the base, and vertical movement of thespindlehead along the column and relative to the base. The support basemay be used to carry a workpiece which is to be operated on by a toolcarried in the selectively positionable, rotatable tool spindle. Atubular quill extends forwardly from the spindlehead both to support theforwardly projecting tool spindle, and to constitute a tubular bearingfor pivotally supporting one end of each one of a pair of extensiblevector members that cooperates to commeasuring members comprises anextensible laser interferometer supported within a separate pair ofcooperating telescoping members, one of which is pivotally secured tothe spindle quill and the other of which is pivotally secured to aspaced apart portion of the base or frame. Thus, each of the laserinterferometers is pivotally secured at one end to the spindle quill andextends in the angularly diverging direction for pivotal attachmenttoward its opposite end to a spaced apart portion of the base. Ineffect, each of the laser interferometers comprises separate membersforming opposite sides of a triangle, the third side of the trianglebeing an imaginary line between the two spaced apart pivot supportportions presented by the base. Irrespective of the vertical andhorizontal position of the spindle within its allowable range ofmovements, the diagonally disposed laser interferometers provide adirect measurement between the axis of the tool spindle and the spacedapart pivot portions of the base.

By applying the Pythegorean theorem twice, the respective vectormeasurements are squared and combined with predetermined offsetdistances between the pivot portions of the base to provide coordinateorthogonal measurements indicating the spindle position along respectivehorizontal and vertical axes of movement. Actually, both vectormeasurements are transmitted to a control system that is disposed toprovide a horizontal measurement of spindle position, and a verticalmeasurement of spindle position. The control system is adapted toreceive horizontal and vertical digital command signals for controllingthe vertical and horizontal servocontrol translators in accordance withhorizontal and vertical feedback error signals initiated by the diagonalvector measurements.

Two different types of vector measurement control circuits are providedfor supplying vertical and horizontal positional control feedback errorsignals.

In one of these two types of controls, digital signals from the vectortransducers are transmitted to a counter and squared, the respectivesquared output from each being transmitted to a summing junction, andwith each summing junction being interconnected to receive apredeterminately modified signal from the other cooperating transducercontrol. Each of the summing junctions is connected to transmit amodified squared signal to separate controls for extracting the squareroot of the prior summed signals. The respective signals from the binarycoded square root control circuits are operative to provide positionalerror feedback signals for the respective X and Y axes of movement. Inaddition, as hereinbefore explained, controlling outputs from the squareroot control circuits are transmitted via branch conductors to therespective input summing junctions adapted to directly receive controlinformation from the command signals.

In the other alternative type of control circuit, separate squaringcontrols are directly connected to be activated by positional inputsignals from the separate vector measurement transducers. The separatesquaring controls are so arranged z-s to directly provide incrementalcontrol changes which respectively represent the difference betweensuccessive square root signals. The arrangement is such as to greatlyexpedite the computational speed of the respective transverse controlsignals by obviating the necessity for separate controls to performsquaring operations and additional cooperating square root controls foreach of the vector measurement inputs. As before, however, the separatesquaring controls are continuously and repetitively modified byconcomitant input signals from the associated vector measurementtransducer in a manner that each squaring control provides theappropriate lineal measurement command signal for the separateorthogonal axes of spindle movement. By means of the describedarrangement, it is possible to achieve more than 300,000 computationsper second to attain a traverse rate of 3 inches per secondsimultaneously following input commands for effecting orthogonalmovements.

It is a general object of this invention to provide a more accurate andimproved machine tool digital control system incorporating vectormeasurement transducers operatively connected to provide positionalfeedback signals for controlling movement along orthogonal axes.

It is a further object to provide position measuring laserinterferometers in a control system for a machine tool to providepositional feedback error control signals to increase machine accuracy.

Another object of the invention is to provide an improved machine toolcontrol system provided with a pair of diagonally disposed vectormeasurement means both pivotally connected at one end to a tool spindleand attheir opposite diverging ends beingpivotally connected to spacedapart portions of a support frame to provide direct vector measurementsof spindle position.

A further object of the invention is to provide a tape control systemincorporating vector measuring transducers coordinately connected toprovide positional error feedback control signals operative to controlmovement along orthogonal axes.

A'further object of the invention is to provide an improved positionalcontrol system for controlling orthogonal movements of a tool spindlehaving a pair of vector measuring interferometers respectively beingpivotally interconnected between the spindle and spaced apart portionsof a frame adapted to support the spindle for power driven movementalong orthogonal axes.

A still further object of the invention is to provide a positionalcontrol system for a machine tool adapted to operate and greatlyincrease the speeds of computation to improve the positioning accuracyof the movable machine toolelement being controlled.

The foregoing and other objects of this invention which will become morefully apparent from the following detailed description, may be achievedby the exemplifying apparatus depicted and set forth in thespecification in connection with the accompanying drawings in which:

DESCRIPTION OF THE DRAWINGS FIG. 1 is a view in front elevation of amachine tool incorporating vector measuring transducers directlyconnected to control power driven movement of an orthogonally movabletool spindle;

FIG. 2 is a view in left side elevation of the machine illustrated inFIG. I and showing the vector measuring means partly in elevation andpartly in longitudinal section;

FIG. 3 is an enlarged fragmentary view, partly in side elevation of atool spindle and a spindlehead support therefor, together with a lasertransducer shown in longitudinal section and comprising one of thevector measuring control means;

FIG. 4 is a view in longitudinal, transverse section through one of thevector measuring transducers, the fixed quill pivot support therefor,and the tool spindle journaled within the quill; the entire view beingtaken along the line 4-4 in FIG. 3;

FIG. 5 is a schematic line diagram illustrating movement of the toolspindle transversely along the horizontal axis, and showing dimensionalchanges in both vector measuring means for the two different spindlepositions illustrated, as well as a fixed offset for the separatetransducer reflectors;

FIG. 5A is a diagrammatic view illustrating the method of utilizing the'vector measurements to achieve orthogonal control;

FIG. 6 is a schematic diagram of a control circuit for utilizing thevector measurements shown in FIG. 5A;

FIG. 7 is a schematic block diagram of a digital control circuitillustrating the interconnection of the separate vector measuringtransducers to provide continuous measuring and error feedback controlsignals for controlling orthogonal movement of the spindle along ahorizontal and vertical axis; and,

FIG. 8 is a schematic block diagram of a vector measuring controlcircuit representing a modification of the circuit illustrated in FIG. 7and showing a simplified method of directly responding to incrementaldifferences between the square and the square root of separate vectorsignals.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring now to the drawings,and more specifically to FIGS. 1 and 2 thereof, the machine tool thereshown incorporates vector measuring transducer means for providingpositional and feedback error control means for controlling positionalmovement of a tool spindle along orthogonal axes. As shown in thedrawings, the machine is provided with a forward work supporting base 18secured to a forwardly spaced foundation 19; and, a rearwardly spacedtool supporting base 21 secured to a like, rearwardly spaced foundation22. The rearward base 21 is spaced apart from the base 18 a distancesufficient to provide an enlarged vertical opening 23 for receiving thevector measuring apparatus 26. In a similar manner, the rearwardfoundation 22 is spaced from the forward foundation 19 by a verticalopening 24 aligned with the enlarged vertical opening 23 between thebases 18 and 21 in a manner to receive the lower end of the measuringapparatus 26. The vector measuring apparatus 26 comprises a pair ofseparate rectilinear measuring transducers 27 and 28 both pivotallysecured at one end to the spindle axis and at their opposite ends tospaced apart G and H pivot axes respectively carried by spaced apartportions of the tool support base 21.

The vector measuring members 27 and 28 comprise position measuringtransducers adapted to continuously and directly measure the respectivediagonal distances between the rotational axis of the tool spindle 50and the spaced apart G and H pivot axes carried by the tool support baseor frame 21. Diagonal measurements from the separate transducers 27 and28 are operatively connected to provide feedback positional errorcontrol signals to a control system in a manner to indicate and controlthe position of the spindle 50 along the X and Y axes of movement.

As shown in FIGS. 1 and 2, it will be apparent that the tool supportbase 21 is adapted to support a tool for movement along the respective Xand Y axes relative both to the base 21 and relative to a workpiececarried by the work support base 18.

To accomplish this, the tool support base 21 is provided with a pair ofspaced apart horizontally extending ways 33 and 34. The lower portion ofan upright column 36 is provided with complementary ways engaging thebase ways 33, 34 and is slidably secured thereto by means of gibs 37, 38respectively secured to the opposite lower edges of the column 36 in theusual manner. For efi'ecting horizontal movement of the upright column36 along the X axis, a depending nut 41 secured to the underside of thecolumn is engaged by a rotatable translating screw 42 driven by a motor43 carried by the tool support base 21.

The upright column 36 is provided with spaced apart vertical ways 45 and46 adapted to support a spindlehead 48 for vertical movement along a Yaxis. To support a tool for selective movement along the X and Y axes,the tool receiving spindle 50 is journaled for rotation about ahorizontal axis in bearings 51 and 52 carried by the spindlehead 48. Aforwardly extending, reduced diameter end of the rotatable tool spindle50 is journaled within a tubular support quill 55 that is integrallyformed with a vertical face plate 56 bolted directly to the frontvertical face of the spindlehead 48. The outer circular surface of thetubular spindle support quill 55 is exactly concentric to the spindleaxis and constitutes an accurate pivot support for one end of therespective vector measuring transducers 27 and 28.

For controlling vertical movement of the tool spindle 50 along the Yaxis, a vertical elevating screw 58 is journaled, to rotate at itsopposite ends in laterally extending upper and lower column portions 36Aand 36B integrally formed with the upright column 36. The rotatableelevating screw 58 extends through a suitable opening formed in thespindlehead 48 and engages an elevating screwnut 60 fixedly securedtherein. Power for rotating the elevating screw 58 to move thespindlehead 48 in a selected vertical direction is derived from a drivemotor 59 carried within the upper portion 36A of the column upright, asshown in FIG. 2.

As shown in FIGS. 2 and 3, the respective vector measuring transducers27 and 28 are secured at one end to a pair of adjacent independentbearings 61 and 62 encircling the support quill 55 for individualpivotable movement. To maintain the bearings 61 and 62 in adjacentrelationship, the support quill 55 is provided with a peripheral grooveengaged by a snapring 63 abutting a side face of the inner race 65 ofthe forward bearing 62. The forward bearing 62 is provided with an outerrace having an integrally formed radial extension 66 to which the upperflanged end of an inner tubular member 68 is secured by means ofcapscrews 69. The inner tubular member 68 comprises the upper portion ofthe vector measuring member 28, and is disposed in slidably extensibleengagement with an outer tubular member 70, the latter being movablysecured to the base 21 for pivotal movement about the H pivot axis.

To support the angularly diverging vector members 27 and 28 for pivotalmovement about the G and H pivot axes, a vector support frame 72 isfixedly bolted to a vertical end face of the tool support base 21, asshown in FIG. 1. The vector support frame 72 is provided with ahorizontally extending arm 72A integrally formed therewith and slightlyspaced from the end face of the base 21 to provide an H pivot support.In a similar manner, the vector frame 72 is provided with a verticallyupstanding arm 72B integrally formed therewith and spaced slightly awayfrom the end face of the base 21 to provide the G pivot axis for theouter end of the vector member 27.

In the enlarged detailed view, FIG. 3, the horizontal vector support arm72A is shown as being provided with an enlarged circular opening 77concentric with the H pivot axis. The outer races of a pair ofantifriction bearings 78, separated by a spacer 81, are disposed withinthe circular opening 77 of the horizontal support arm 72A and inposition to engage an inwardly extending shoulder 80. A laterallyextending circular hub 79 is integrally formed with the outer tubularmember 70. The vector member hub 79 is supported by the frame supportarm 72A for pivotal movement by the antifriction bearings 78 andretained in engagement therewith by a snapring 82 engaging an annulargroove formed in the hub. A cover plate 83 is secured to a side face ofthe horizontal support arm 72A in a position to function as an enclosurefor the circular opening 77 and the bearings contained therein.

For simplicity in the description, the member 28 is designated as avector measuring member or transducer. Actually, the vector measuringmember 28 may comprise any of the commercially available, rectilinearmeasuring transducers operably interconnected to measure the rectilineardistance between the spindle axis and the H pivot axis, as shown in FIG.3. In a preferred form of the invention, the vector measuring member 28comprises a fringe counting laser interferometer operatively carriedwithin the cooperatively disposed, relatively extensible tubular members68 and 70.

As shown in FIGS. 3 and 4, and as hereinbefore explained, theinterconnected telescoping tubular members 68 and 70 enclose a laserinterferometer operative to precisely measure the distance between thespindle axis and the H pivot axis during bodily movement of the toolspindle 50. The interferometer carried within the extensible tubularmembers comprises essentially a first prismatic element 85 fixedlysecured within the outer tubular member 70 and provided with a lighttransmissive base 86 perpendicular to the axis of movement thereof. Alaser 88 shown in fragmentary form in FIG. 4 is carried by the outertubular member 70 in a position to project an intense beam of light 89toward an angular side face of the prismatic element 85. Although notshown in detail, the laser 88 is preferably a helium neon gas laserhaving an activating plasma tube positioned between spaced end bracketssecured to a tubular housing, and is connected in the usual manner to beelectrically energized by a source (not shown). The laser 88 is spacedfrom the side face of the prismatic element 85 by a tubular spacer 87.At its'inner end the laser 88 is provided with a combined sphericalreflector and collimating lens 91 adapted to project outwardly anintense coherent beam of collimated monochromatic light toward theangular, light transmissive face of the prismatic element. The prismaticelement comprises a modified form of double image Koesters prismprovided with a semitransparent, beam splitting interface 93 disposed inperpendicular relationship to the base 86. Thus, the input beam 89 isdivided by the beam splitter 93 into a transmitted beam 94 and areflectively returned, fixed length reference beam 95. The transmittedbeam 94 is reflected by an internal angular face 96 of the prismaticelement 85, and reflected outwardly to constitute a variable lengthmeasuring beam 94V. A retroreflector 98 fixedly secured within the innertubular element 68 is adapted to receive the outwardly projected beam94V and reflectively return a coincidental beam along the same path asthe transmitted beam for recombining at the beam splitting interface 93.The retroreflector 98 presents a beam reflecting face perpendicular tothe axis of the tubular member 68 and radially spaced at predetermineddistance relative to the axis of the spindle 50. The arrangement is suchthat both the transmitted beam 94V and the coincidental beamreflectively returned by the retroreflector 98 are parallel to thelongitudinally extending axis of both tubular members 68 and 70irrespective of the extensible movement therebetween.

To provide directional sensitivity in fringe counting measurements, aninternally stepped reflector 102 is secured to the base of the prismaticelement 85 in a position to receive the internally directed, fixedlength reference beam. As shown in FIG. 4, the reference beam reflectedby the interface 93 is again reflected by an internal angular reflectivesurface 101 and directed along a path illustrated by the beam 95R towardthe internally stepped reflector 102. The reflector 102 is provided withadjacent, stepped reflective surfaces 103 and 104 respectively disposedto shift adjacent beam portions by onefourth of a wavelength to returnphase differentiated beam portions along a path coincidental with thebeam 95R. The reflectively returned beam portions are again reflected bythe internal angular reflective surface of the element 85 and directedtoward the interface 93 where they are recombined with thecoincidentally returned, variable length measuring beam 94 to providephase differentiated interference fringes.

Upon recombining of the coincidentally returned measuring beam andreference beam portions at the interface 93, there are provided phasedifferentiated portions of interference fringes 107 and 108 respectivelytransmitted to activate photodetectors 109 and 110 adhesively secured toan external side face of the prismatic element 85. The interferencefringe portions 107 and 108 are provided with a difference in wavelengthto provide a sensitivity to direction of movement as well as accuratelymeasuring the distance traversed.

As described in connection with FIGS. 3 and 4, the vector measuringmember 28 comprises a laser interferometer carried within the extensibletubular members 68 and 70 for mt asuring the exact distance between thespindle axis and H pivot axis. In a similar manner, the vector measuringmember 27, shown in FIG. 1, comprises a pair of telescopic, tubularmembers 113 and 114. In like manner also, a laser measuringinterferometer (not shown) is operatively disposed in the extensible,tubular members 113 and 114 for accurately measuring the existingdiagonal distance between the spindle axis and the G pivot axis. In viewof the similarity between the laser interferometers carried within therespective vector measuring members 28 and 27, however, it is not deemednecessary to show or describe in detail the interferometer within themember 27. The mode of operation and disposition of parts of therespective interferometers are identical, and both function to providepositional indicating signals for indicating the respective distancesbetween the spindle axis and the cooperating G and H pivot axes duringbodily movement of the tool spindle along the X and Y axes of movement.

As will hereinafter be more fully explained, there is provided apositional control system operative to control bodily movement of thetool spindle along the X and Y axes in in accordance with direct vectormeasurements between the spindle axis and the G and H pivot axesrespectively.

As shown in FIGS. 1 and 2, the forwardly spaced work support base 18 isprovided with spaced apart horizontal ways 64 and 67 adapted to slidablysupport a saddle 69 for horizontal movement. A pair of gibs 71 securedto the opposite outer edges of the saddle 69 engage the underside of therespective ways 64 and 67 to guide the saddle for Z axis movementrelative to the column 36. A worktable 75 carried by the saddle 69 isadapted to support a workpiece (not shown) in operative relationship toa tool carried by the tool spindle 50. Thus, the worktable is movablealong a horizontal Z axis in coordinated relationship with movement ofthe tool spindle 50 along the X and Y axes. For selectively moving theworktable 75, a motor 76 secured to the base 18 drives a screw and nuttranslator (not shown) connected in well-known manner to move the saddle69 along the support ways 64 and 67.

In F IG. there is diagrammatically illustrated the relationship betweenthe vector measuring members 27 and 28 and the axis of the tool spindle50, with the spindle being represented in two different positions. Theposition of the tool spindle 50 is represented with respect to thecoordinate vertical Y axis and horizontal X axis respectively. The firstposition of the tool spindle 50 is illustrated by the dashed linesinterconnected between the tool spindle and the respective measuringbeam originating interferometers 27 and 28. The second position of thetool spindle is represented by the broken lines interconnected betweenthe spindle (identified as 50') and the respective G and H pivot axesassociated with the interferometers 27 and 28. In both the first andsecond positions of the tool spindle illustrated in FIG. 5, the verticalY distance from the horizontal X axis is identical. Thus, in movingrightwardly from the first to the second position, only the X distanceis changed. During such rightward horizontal movement, however, both ofthe diagonal pairs of vector measurements are changed as indicated bythe dashed lines and broken lines respectively.

With the spindle 50 in its first position illustrated in FIG. 5, theprismatic element 85 of the interferometer 28 is so pivoted relative tothe H pivot axis as to project a laser measuring beam RB toward thecooperating optically aligned retroreflector 98. As hereinbeforeexplained, the tubular, extensible interconnection between the prismaticelement 85 and retroreflector 98 effects appropriate pivotal movement ofboth to maintain proper alignment therebetween for receiving andreturning a coincidental beam RB toward the prismatic element 85.Simultaneously therewith, a prismatic element 118 associated with theinterferometer 27 is so pivoted relative to the G pivot axis as toproject a laser measuring beam RA toward a cooperatively disposedretroreflector 119 comprising the cooperating portion or prismaticelement of the interferometer 27. As indicated in FIG. 5, it will beapparent that the retroreflector 119 is pivotally positioned relative tothe pivot axis of the spindle 50 for reflectively returning acoincidental beam RA toward the prismatic element 118 because of theextensible tubular interconnection. With these conditions existing, thefringe counting interferometers 27 and 28 are respectively operative toaccurately indicate the diagonally measured, lineal distances RA and RBrespectively illustrated as interconnected between the spindle axis andthe G and H pivot axes on the machine base.

With the tool spindle moved rightwardly to the second positionillustrated in FIG. 5, the positions of the respective interferometers27 and 28 are changed as indicated by the broken lines, and as indicatedby the suffix prime after several of the reference numerals. With thespindle 50 displaced rightwardly, the respective prismatic element 85'and cooperating retroreflector 98' comprising the interferometer 28 arepivoted to project and coincidentally return the fringe countingmeasuring beam RB. In a similar manner, with the spindle in itsrightwardly moved position, the prismatic element 118' and cooperatingretroreflector 119' comprising the interferometer 27 are pivoted toappropriate positions for pro- 5 jecting and coincidentally returningthe fringe counting measuring beam identified as RA. With the spindle inits second position in FIG. 5, it is emphasized that the cooperating andtelescopingly interconnected portions of the interferometers 27 and 28are identical, but have been merely pivoted to positions appropriate tothe changed horizontal position of the tool spindle.

During operation of the machine incorporating the vector measuringposition control apparatus of the present invention, both of the vectormeasuring members 27 and 28 are continuously operative to provideseparate vector measuring beams, such as RA and RB described inconnection with FIG. 5. As will hereinafter be more fully explained, thevector measuring beams RA and RB cooperate to provide orthogonallydisposed separate X and Y signals that continuously indicate spindleposition along the X and Y axes. Whenever the numerical input commandsignal requires horizontal spindle movement, such as movement from thefirst to the second position in FIG. 5, different horizontal X commandsignals are provided to effect the required movement, with the verticalY command signals remaining the same. A numerical control system isarranged to supply orthogonal input command signals that are compatiblewith the respective X and Y position indicating signals resulting fromseparately combining the fringe counting measurements from therespective beams RA and RB. With the vector measuring signals RA and RBbeing continuously utilized to provide compatible orthogonal X and Ysignals, there are provided error command signals representing thedifference between the spindle actual and numerically commandedposition. Depending upon the orthogonal input command signals,therefore, the resulting error command signals are operative to effectservo-controlled translating movement of the spindle 50 along the X andY axes as may be required.

To better illustrate the method of utilizing vector measurements toprovide the necessary orthogonal feedback signals, FIG. 5Adiagrammatically illustrates the G and H pivot positions with respect tothe axis position of the spindle 50. Although no structure per se isrepresented in FIG. 5A, the vector measuring beams RA and RB associatedwith interferometers 27 and 28 are shown as continuously measuringseparate orthogonal signals giving X and Y axis positions. The verticalor Y axis is represented as extending from north to south, andintersects the horizontal or X axis which extends from east to west. Thesolid line portion of the Y axis and the solid line portion of the Xaxis delineate a quadrant within which the tool spindle 50 is movablerelative to the spaced apart G and H pivot axes. Thus, the solid lineradii X and Y delineate a first or NE quadrant within which the toolspinr'le 50 is selectively movable along any combination of axes. In asimilar manner, the spaced apart pivot axes G and H of the respectiveinterferometers 27 and 28 are within the third or SE quadrant in themanner that interferometric vector measurements are available even whenthe spindle 50 is moved into proximity to the intersection of the X andY axes. The particular locations shown for the spindle axis, as well asthe G and H pivot axes are for illustrative purposes. It will beunderstood that other locations may be used for these axes withoutinterfering with operation.

To facilitate explaining the derivation of the separate orthogonalposition indicating error signals, separate delta and sigma trianglesare illustrated in FIG. 5A. The delta triangle comprises adjacentperpendicular legs designated as having values of delta 3 and delta 4with the hypotenuse being designated as delta 5. For this disclosure,the vector measuring beam RA, extending between the axis of the spindle50 and the G pivot axis is considered equivalent to the delta 5hypotenuse of the delta triangle in FIG. 5A, in spite of the offsetsbetween the opticalelements and the respective pivot axes. That leg ofthe delta triangle designated as having a delta 4 value actuallycomprises two values including a positive or variable X spindle positionplus a (A) or fixed value extending between the Y axis and a lineindicated as parallel thereto and extending through the G pivot axis.Incidentally, those values rightward or west of the vertical Y axis havea positive or plus value, as indicated in FIG. A, and those valuesleftward or east of the Y axis are negative In a similar manner, allvalues above or north of the horizontal X axis are positive in value andthose values below or south of the horizontal X axis line are negativein value.

Referring again to the delta triangle in FIG. 5A, the delta 5 hypotenusethereof continuously representing the RA vector measurement being known,it is necessary to obtain the horizontal value for the X spindleposition designated by the dashed line extending between the spindle 50and the vertical Y axis. The X spindle position is necessary to developan error command signal according to the horizontal input command signalfrom the control system, and compatible with the servo translator forefi'ecting X axis movement. In addition to the vector value RA, severalother values for the two legs of the delta triangle are likewise known.As hereinbefore explained, the delta 4 leg of the triangle equals X (A)representing the leftward or east offset of the G pivot axis. That legof the triangle designated as having a delta 3 value extendsperpendicularly upward from the G pivot axis. The delta 3 leg of thistriangle comprises the fixed value (B), representing the negative offsetof the G pivot axis, plus the vaIue Y, or the present existing positionof the spindle 50 along the vertical Y axis. Therefore, the delta 3 legof the triangle can be designated as (Y -B). Thus, in both the delta 3and 4 legs of the triangle, the only fixed values are (B) and (A)respectively.

In a similar manner, the sigma triangle is represented as provided witha hypotenuse indicated as sigma 5 which is the RB vector measurementdelineating the distance between the spindle axis and the H pivot axisfor the interferometer 28. The vertical leg of the sigma triangle isdenoted as having a value of sigma 4 comprising the Y spindle positionplus the fixed offset (-D) value representing the distance of the Hpivot axis downwardly from the horizontal X axis. The lower horizontalleg of the sigma triangle is indicated as having a value of sigma 3representing the distance between the H pivot axis and a line extendingperpendicularly downward from the axis of the tool spindle 50. The sigma3 leg of the triangle comprises the existing (X) distance plus theoffset (-C) indicating the fixed distance of the H pivot axis leftwardlyfrom the vertical Y axis. Thus, the sigma 3 leg of the sigma triangleequals (X-C).

Depending upon the input command signals from the control system foreffecting selected movement of the spindle 50, the values for thehorizontal X spindle position and vertical Y spindle position may beselectively changed. In view of this,

the only fixed values for the sigma triangle are the (D) offset in thevertical leg, and the (C) offset value in the horizontal leg. With theRB vector measurement together with the offset values (C) and (-D) ofthe sigma triangle known, it is necessary to obtain the X positionalsignal for the spindle 50 along the horizontal axis. In view of the factthat the vertical and horizontal position of the tool spindle 50 ischanged in accordance with numerical input command signals from thecontrol system, it will be apparent that each leg of the respectivedelta and sigma triangles will be changed according to the change inposition of the tool spindle. Thus, the identifying values 3, 4 and 5respectively associated with the delta and sigma triangles have beenused only for illustrative purposes in designating the correspondingsides of the respective triangles.

To facilitate following the various designations for positioning thetool spindle 50, FIG. 5A includes the Pythagorean theorems for obtainingthe vertical Y and horizontal X positions of the tool spindle. As thereindicated, RA of the delta triangle equals (XA-)+( YB) Consequently, Yequals B plus the square root of [RA (XA In a similar manner, R19 of thesigma triangle equals (XC)*+( Y-D). As a result,

the horizontal position of the spindle 50 is represented by the formulaX equals C plus the square root of [RB*( YD)].

As shown in FIG. 6, there is represented in simplified diagrammatic forma control circuit for utilizing the separate vector measurements RA andRB as input command signals to provide coordinate servo-controlledmovement along the respective transverse X and Y axes. The fringecounting measuring beam signal RA is transmitted to a squaring control123 operative to continuously square the vector input signal. From thecontrol 123, the continuously squared signal RA is transmitted to asumming junction 124 which is simultaneously connected via an inputconductor 126 to continuously receive a modifying signal (X-A)originating with the RB vector signal. Both of the input signalsreceived by the summing junction 124 are added to provide one signal andtransmitted therefrom by an output conductor 127 to a square rootcontrol 128 that is operative to continuously extract the square root ofthe combined signals supplied thereto. The square root and the resultingvalue,

control 128 is connected via a conductor 131 to transmit thecontinuously pulsating square root signal to a summing junction 132 thatis simultaneously connected to receive a fixed pulse input signal B andcorresponding in magnitude to the fixed offset for the G pivot axis, asillustrated in FIG. 5A. The summing junction 132 is operative to combinethe variable square root signal received from input conductor 131 andthe fixed pulse input signal B to provide a continuous output signalthat functions to continuously indicate the vertical or Y position ofthe tool spindle. The existing Y position signal is transmitted viaconductor 134 to the error output command 135 that is simultaneouslyconnected to receive a numerical digital or tape input command signalindicated as the Y command and being operative to effect the requiredvertical spindle movement along the Y axis. Conductor 136 is connectedto transmit an error command signal of proper polarity for effectingdirectionally controlled actuation of the Y axis servodrive 137; andcomprising the differencebetween the Y tape command signal and the Yerror command along the input conductor 134. The error command signalalong the conductor 136 effects movement of the spindle the requireddistance along the vertical or Y axis.

Simultaneously with effecting Y axis movement, the conductor 134 isconnected via a depending conductor 140 to provide a signal forpredeterminately modifying the concomitant vector control signal RB. Thepositive Y position input signal from the conductor 140 is transmittedto a summing junction 141 that is connected to receive a minus D inputsignal of fixed value corresponding to the fixed vertical offsetposition of the H pivot axis as indicated in FIG. 5A. As previouslyexplained, the variable value of (+Y) is combined with the fixed inputvalue of (D) by the summing junction 141 in the case (Y-D) istransmitted by conductor 142 to a squaring control 145. In a mannersimilar to that before described, the squaring control 145 functions tocontinuously square the input value to provide an output value of (Y-D)which is transmitted via conductor 146 to another summing junction 150interconnected in the position indicating control for the X axis.

At the same time, the fringe counting measurement signal RB istransmitted to a squaring control 151 which is operative to provide acontinuously squared, pulsating output signal via conductor 152 fortransmitting the value (RB)"- to the summing junction 150. The twovariable inputs schematically illustrated as being supplied byconductors 146 and 152 are added by the summing junction 150 andtransmitted therefrom along an output conductor schematically indicatedat 153 connected to a control 154 operative to continuously extract thesquare root of the combined input signal. The continuously pulsatingoutput signal from the square root control 154 is transmitted by aconductor 155 to another summing junction 158 connected to receive afixed pulse input signal (C) corresponding to the fixed horizontaloffset position of the H pivot axis in FIG. 5A. The summing junction 158is disposed to add the pulsating input signals to provide a combinedout- 1 put signal via conductor 159 for indicating the horizontal or Xposition of the tool spindle. The existing X position signal istransmitted by conductor 159 to an error output command 160 that isconnected to receive a digital numerical or tape input command signalfor controlling X axis movements.

From the error output command 160, an error signal is transmitted byconductor 161 for actuating an X axis servodrive 162 to effect thenecessary and required horizontal movement along the X axis. v

As this occurs, a value corresponding to the X axis position istransmitted from the conductor 159 along a conductor 165 connected toprovide a positive input signal to a summing junction 166.Simultaneously, the summing junction 166 is connected to receive acontinuously pulsed signal (A) corresponding to the fixed horizontaloffset of the G pivot axis, as shown in FIG. A. The resulting combinedsignal (X-A) is transmitted along conductor 167 to a squaring control168 adapted to provide a continuous output having the value (X-A)transmitted along conductor 126 to provide the modifying input signal tothe summing junction 124.

The logic relationships between various portions of the control circuitfor converting spindle position vector measurements, such as RA and RB,are illustrated in FIGS. 5A and 6. As hereinbefore explained, anumerical input command to effect movement along one single axisoperates to provide position indicating feedback signals from both theRA and RB vector measuring beams to activate both of the squaringcontrols 123 and 151. For example, 2 inch numerical input command to theerror command control 135 will operate to actuate the Y axis servodrive137 for effecting a 2 inch vertical movement. In the absence of X inputcommands to the error command control 160, the X axis servodrive 162will merely function to dynamically retain the spindle in its existing Xaxis position while the 2 inches of vertical Y axis movement is takingplace. During such a 2 inch Y command, the RA vector measuring beamactuates the squaring control 123 to initiate a signal modified by theinput via conductor 126, for effecting 2 inches of movement along the Yaxis. As previously explained, the Y positional signal initiates amodifying control along conductor 146 to the summing junction 150connected to receive the input from the vector measuring beam RB. Thus,during such a command for 2 inches of vertical Y axis movement, theinput from conductor 146 to the summing junction 150 counteracts thesimultaneous RB vector signal from the conductor 152 thereby obviatingany output signal for effecting X axis movement. As the commanded Y axismovement is being effected, however, it will be apparent that the vectormeasuring beam RB is continuously changing in corresponding changedrelationship to an opposite change in the modifying signal transmittedfrom the Y position indicating conductor 134 to the summing junction150. Likewise, during such a described 2 inches of movement along the Yaxis, modifying signals will be available from the input conductor 126in spite of the fact that no X position signal for movement is availablefrom the conductor 159. v

The simplified diagrammatic circuit drawing of FIG. 6 is provided simplyto implement the logic and mathematical relationships explained inconnection with FIG. 5A for developing the orthogonal command signals.For purposes of explaining the operation of this invention, it is notdeemed necessary to describe in detail the various gating controls andshift registers which would be required for effecting positionallycontrolled movement along either the X or Y axes. Again assuming aninput command for effecting 2 inches of Y movement with no X movementbeing required, the Y'axis servodrive 137 is operated to effect 2 inchesof movement in a selected direction with the X axis servo 162functioning merely to dynamically retain the spindle in its existing Xaxis position. After the selected Y axis movement is efiected, bothservos 137 and 162 would function merely to retain the spindle in itsselected position with the Y and X error command controls 135 and 160being available for receiving the next input command signals foreffecting the next required movements. In cf fecting the described 2inches of vertical Y axis movement, a predetermined number of pulsescorresponding to light fringe signals from the respective measuring beaminterferometers are supplied to equal a cumulative total of 2 inchesalong the Y axis. Each light fringe equals 6.25 micro inches or 6%millionths of an inch. Depending upon the selected direction ofmovement, the control system is operative to increment or decrement thetotal error command pulses for effecting movement to the commandedposition in the selected direction.

In FIG. 7 there is represented an expanded block diagram illustratingthe source and distribution of the fixed pulse trains corresponding tothe offset positions for the respective G and H pivot axes of theinterferometers 27 and 28 as described in FIG. 5A. In FIG. 7 there islikewise illustrated the method of interconnecting controllerscomprising shift registers for squaring the respective RA and RB vectormeasurements, summing the squared values-with variable pulse traininputs, and then extracting the square root of the summed inputs of thepulse trains. Selective control of bidirectional movement along the Xand Y axes is likewise illustrated as available due to the phasedifferentiated input signals from the vector measuring interferometers27 and 28 respectively.

As schematically shown in FIG. 7, input commands for effecting selectedmachine movements are derived from a numerical control system 166,preferably provided with a punched command tape movable relative to atape reader (not shown) in well-known manner to provide a source ofdigital input command signals for effecting the various digitallycontrolled movements. As known in the art, the punched tape commandscomprise blocks of predetermined input data for effecting the availablemachine functions in the required sequence. Such input command signalsare adapted to provide commands as to spindle speed rate, feed rate, andextent of positional movement along the X, Y and Z axes respectively. Ashereinbefore explained, this invention is directed principally to thederivation of orthogonal positional indicating signals to establish thebasis for effecting error command of spindle movements in response tocontinuous vector measurements of spindle position. To accomplish this,a unified control system is provided for continuously translating vectormeasurements of spindle position into separate orthogonal pulse trainsignals indicating spindle position along the X and Y axes. Theservomotors are then actuated to selectively move the spindle along therespective axes in accordance with error signals comprising thedifference between the axial input tape command signals and the axialposition signals derived from the positional vector measurements. Theextent of movement to the selected X and Y positions is determined bythe total number of digital pulses, and the speed of moving to thepreselected positions is determined by the frequency of thepredetermined positional command pulses comprising the X and Y commands.

As schematically shown in FIG. 7, the numerical control system 166 isconnected via conduit 167 to selectively actuate a spindle rate control169 for operating the tool spindle 50 at a predetermined rate, or forstopping spindle rotation. Likewise, the control system 166 is adaptedto provide a digital control signal along a conduit 171 connected toprovide Z axis commands 172 for moving the worktable 75 at a selectedrate and direction of movement along the Z axis, or for stopping tablemovements. In a similar manner, the control system is connected totransmit positional and rate control commands along a conduit 174connected to actuate a Y axis control command register 175 connected viaa conduit 176 to provide positional control data to a Y axis digitalservo error controller 178. In addition, the numerical control system166 is connected via a conduit 182 to supply rate and position commandsto actuate an X axis command register 183 connected via a conduit 184 tosupply a positional command signal to an X axis digital servo errorcontroller 186.

With the various shift registers 169, 172; 175 and 183 supplied with thenecessary input command data, an end of block or sequence control signalfrom the numerical control system rows of holes representing in binaryform various numerical instructions for the various functions available.After each.

succeeding group orgroups of-words comprising the command data foreffecting machinefunctions, the, tape is punched with an end of block orsequencecontrol signal. Each such sequence control signal is connectedto actuatethe machine by means of a controller (not shown) to actuatethe machine for perfonning the command functions stored immediatelyprior to that particular sequencesignal. Inasmuch as the end of block orsequence signal for effecting machine functions in accordance withstored datais known, it is not deemed necessary to showindetail thevarious gating com-. mand signals for accomplishing the functions to beperformed.

As will be explained, the X'axis position register 189-and the Y axisposition register 190 are adapted to provide signals for indicating theexisting position of the tool spindle 50 along the respective X and Yaxes in the form of a digital pulsed signal compatible with the commandsignals respectively transmitted to the X and Y shift registers 183and175. Existing, X axis position signals are transmitted from .the Xregister 189 viaa conduit 192 to the X axis digital controller 186. Thedifference between the X axis command signal via conduit 184 .v

and the existing X axis position signal via conduit 192 operate toactuate the X axis digital servocontrol 186 for providing an outputerror signal along conductor 193 to effect the required directionallycontrolled movement of the X axis servomotor 43.

In a similar manner, the difference between the Y command signal alongconduit 176 and the existing Y axis position signal along conduit 195actuates the ,Y axis digital servocontroller 178 to provide an errorsignal along the conductor 196 for effecting actuation of the Y axisservomotor 59 to move the spindle the required distance along the Yaxis. Thus, depending upon the input command signals and the inputposition signals, the respective digital servocontrollers 178 and 186are operative to efi'ect the required directionally controlled movementof the servomotors 59 and 43 for moving the spindle to selectedposition.

The usual source of electrical energy (not shown) is connected toenergize the laser for the interferometer 28, as well as the phasedifferentiated photodetectors 109 and 110 associated therewith. Ashereinbefore explained, with reference to FIG. 4, the photodetectors 109and 110 are energized to provide fringe signals in quadrature spacedrelationship, upon relative movement between the beam splitting Koestersprism 85 and the axis of the spindle 50. Thus, upon telescoping movementof the interferometer 28 in either direction relative to the spindle,fringe counting signals are transmitted from the respectivephotodetectors 109 and 110 via output conductors to energize Schmitttriggers 201 and 202 respectively. The signals are then transmittedviaconductors 203 and. 204 toa synchronizer 207 connected to maintain theproper phase difference therebetween and operative to transmit phasedifferentiated, direction indicating signals via conductors 209 and 210to a counter 212. The counter 212 comprises a shift register operativeto provide pulsating light fringe signals that, continuously indicatethe total vector distance between the pivot axes including the length ofthe vector measuring beam RB plus the fixed offsets at the opposite endsof the beam. Inasmuch as a laser interferometer is a preferred vectormeasuring device, each light fringe would have an incremental value of6% millionths of an inch. This invention, however, is not restricted tolaser interferometers for vector measurements,

nor is it restricted to pulses having thevalues specified. Obviously,other types of measuring transducers can be utilized to provide vectormeasurements, and the pulses can be of other predetermined values.

Depending upon the direction of extensible movement of t theinterferometer 28, the counter 212 is adapted to provide continuouslysquare the total number of pulses comprising the position indicatingvector beam RB. From theRB squaring control 218,-the successivesquaredsignals are transmitted via a conduit 220 to asummingregister221. Thesumming register 221 isconnected via another input conductor 223to receive a continuous, variable pulsed signal from an auxiliarycontrol 224. As will hereinafter be more fully explained, the variable.pulsed signal from the control 224' varies in accordancewith changes inthe vector measurement effected by the laser interferometer 27.. Thesumming register 221 .is operative to continuously add the total signalssupplied by the separate input conductors 220 and 223, and is connectedto transmit the continuously changing total signal via a conduit 227'toa controller 228as schematically indicated in FIG. 7. The controlcircuitwithin the controller 228 is operative to extract the squarerootof the summed input supplied via input conductor 227, and transmit thereduced or square root of the summed input via a conductor 229 toanother summing unit 231. At the same time, a pulse divider 235 isoperative to provide a fixed pulse output signal having a (-C) valuecorresponding to. the numerical value of the horizontal offset for the Hpivot axis, as shown in FIG. 5A. The fixed pulse output (-C) istransmitted via a conductor 234 to the summing unit 231 which functionsto add the fixed pulse input to the variable pulse input received viainput conductor 229, and is connected via an output conduit 237 toprovide the resulting position indicating signal to the X axis positionregister'189.

In addition to supplying a positional signal for continuously actuatingthe X axis position indicating register 189, the output conductor 237 isconnected to supply a signal of like pulsating value via a branch outputconduit 239 to a controller 240 adapted to proportionately modify the Yaxis position indicating signal.

In addition to receiving a positional command signal equal to the Xposition via input conductor 239, the controller 240 is connected'via aninput conductor 242 to a pulse divider 243 operative to supply a fixedpulse output signal having a value of (A) that is equal in value tothefixed horizontal ofi'set (-A) of the G pivot axis shown in FIG. 5A.The pulse control divider 243 is connected'via a conductor 245 to beenergized by a pulse train generator or clock'246 that is likewiseconnected via an output conductor 248 to energize the pulse divider 235for-effecting the fixed value (-0) signal. The clock 246 likewiseprovides pulse trains via conductors 250 and 251 respectively connectedto energize pulse controlling dividers 253, and 254 for providing (-8)and (-D) signals-Actually, the clock 246 maintains the propersynchronism between all portions of each of the circuits illustrated inboth FIGS. 7 and 8 pulsating signal (-8) is transmitted by a conductor256 which is connected to supply a fixed pulse input signal to a summingunit 257 for determining the orthogonal Y axis position. At the sametime, the controller 240 is connected to continuously square the valueof the input signals (X-A) to provide a squared signal along an outputconductor 258. Thus, a variable pulsed signal control 259 is activatedby the conductor 258 andconnected to provide an output signal alongiaconductor 260,for providing one variable input to a summing register-263 operative to control Y axis position.

In a similar manner, the pulse train divider 254 is operative totransmita pulsating signal of a (-D) value via a conductor 264-to anintermediate controller 265 that is simultaneously connected to receivean input signal via a conductor 267. The fixed pulse signal (-D) isequal to the numerical value of the vertical (-D) offset forthe H pivotaxis as shown in FIG. 5A.

As schematically illustrated in FIG. 7, the value of the pulsatingsignal from conductor 267 varies in accordance with a variation in theorthogonal Y position of the tool spindle as determined by the Y axissumming unit 257. The controller 265 is operative to continuously squarethe sum of the input signals received via conductors 264 and 267, andoperates to provide a pulsating output signal having a value of (Y-D)squared which is transmitted along an output conductor 268 connected toprovide the variable pulsed signal 224. In addition to the variablepulsed signal 224 for modifying the X axis position signal, the pulsegenerating clock 246 is connected via the conductor 248 to energize thepulse train divider 235 which is connected via conductor 234 to transmita fixed value pulsating output signal (C) to the summing unit 231, ashereinbefore explained.

For effecting the pulsating measurement of the RA vector beam, thetransducer 27 is provided with a pair of photodetectors 271 and 272secured to the unitary prismatic element 118. In a manner similar tothat hereinbefore described for the transducer 28, the photodetectors271 and 272 of the interferometer 27 provide phase displaced lightfringe signals. The

photodetectors 271 and 272 are respectively connected by as 4 sociated'conductors to transmit the directional indicating fringe signals toSchmitt triggers 273 and 274 that are, in turn, connected viarespectively associated conductors 277 and 278 to energize asynchronizer 280. From the synchronizer 280, the phase differentiatedsignals are transmitted via output conductors 283 and 284 to actuate acounter 285 adapted to continuously indicate the total number of fringecounting signals comprising the vector measuring beam RA to indicate thedistance between the pivot axes. Depending upon the sequence in whichthe conductors 283 or 284 are being energized to transmit signals by thesynchronizer 280, the counter 285 is operative to increment or decrementthe pulsating RA vector measuring signal. From the counter 285, outputcontrol signals indicating the value of the vector measuringbeam aretransmitted via output conductors 287 and 288 connected to supply inputsignals to a controller 289. The controller 289, in turn, is operativeto continuously square the value of the RA signal transmitted theretofrom the RA counter 285. Successive RA squared signals from thecontroller 289 are transmitted via an output conductor 290 to thesumming register 263.

In the event the RA vector beam is increasing in rectilinear length, thesynchronizer 280 operates to provide pulsating output signals toincrement the value of the RA signal within the counter 285.Consequently, an RA signal of increased value, or increasing value, istransmitted along the positive conductor 288 to effect an increase inthe (RA) squared signal effected by the controller 289.

The summing register 263 operates to add the total value of the (RA)squared signal from the input conductor 290 to the variable pulse signalreceived from the control 259 via the input conductor 260. The combinedsignal from the summing register 263 is then transmitted via an outputconductor 293 to a controller 294 operative to continuously extract thesquare root of the combined signals successively submitted thereto. Thepulsating values of the successive square root signals from thecontroller 294 are then transmitted by an output conductor 295 to asumming unit 257 for determining the vertical Y position. In addition tothe square root signal from the controller 294, the summing unit 257receives via the input conductor 256 a fixed pulse signal having thevalue (B) as indicated for the vertical offset position of the G pivotaxis in FIG. 5A.

As hereinbefore explained, it is not deemed necessary to show in detailthe various shift registers, gating circuits or other control elementsrequired to trigger the numerical control system to actuate theservomotors for effecting movements according topredctermined inputcommand signals. The control circuit schematically illustrated in blockdiagram form in FIG. 7 is deemed fully adequate to explain theinterrelationships effected by the principal shift registers and controlelements, as well as the logic relationships necessary to effectivelytranslate the separate vector measurements of spindle position intocorresponding orthogonal measurements of spindle position. Further, theblock diagram of FIG. 7 together with the diagrammatic views of FIGS. 5and 5A illustrate the method of translating vector measurements intoorthogonal measurements and utilizing the resulting orthogonalmeasurements as feedback error control signals for controlling movementof the spindle along a horizontal X axis and a Y axis in response tonumerically commanded power translators to effect such movements. g I

Attention is directed particularly to the fixed offset measurements ofthe G and H pivot axes for the outer ends of the respectiveinterferometers as shown in FIG. 5A. To facilitate the description, thetwo fixed offset measurements respectively associated with each pivotaxis are represented by alphabetic letters instead of numerical values.As hereinbefore explained, the, horizontal (A) offset and the vertical(B) offset for the G pivot axis associated with the RA vector measuringbeam can be directly expressed in numerical values, each of which can betranslated into an actual number of the value of total light fringesequal to the respective (A) and (B) offsets. In like manner, thehorizontal (C) offset and the vertical (D) offset for the H pivot axisassociated with the RB vector measuring beam can be converted intonumerical values which, in turn, can be translated into a total numberof light fringes equal to the exact offset positions. Although notessential, the respective alphabetic letter values are usuallyrepresented in terms of the total value of the light fringes for each ofthe rectilinear offsets to provide respective pulse trains having apredetermined fixed value that are completely compatible with the valueof the total number of light fringes generated in other portions of thecontrol circuit.

At the very outset, therefore, the pulse dividers 243, 253, 235 and 254are respectively connected to provide fixed pulse outputs schematicallyillustrated as having outputs which correspond to the various offsetsillustrated in FIG. 5A. For purposes of illustration, it will now beassumed that the tool spindle 50 has been bodily moved to a zero inchposition along both the horizontal X axis and the vertical Y axis. Itwill likewise be assumed that the 250 KC. clock generator 246 has beenactivated to supply the appropriate values of fixed pulses to therespective pulse dividers 243, 253, 235 and 254. With the transducers 27and 28, as well as the X and Y axis servomotors 43 and 59 alsoenergized, control signals are immediately available from the X and Yaxis position registers 189 and 190 to activate the respective servoerror controllers 186 and 178 for dynamically retaining the servomotors43 and 59in the zero axis position.

With these conditions existing, a control tape in the numerical controlsystem 166 is operated to transmit a 5 inch Y position command signal tothe tape command register and a like 5 inch X command signal to the tapecommand register 183. With the separate 5 inch positional commandsignals transmitted to the command registers 175 and 183, the tapewithin the system 166 is advanced to read the end of block signal toimmediately activate the entire control system for effecting theseparate 5 inch X and Y axis movements. With the system thus triggeredfor effecting spindle movement, the selected 5 inch input commands aretransmitted to the respective Y and X axis servo error controls 178 and186 for providing output signals along conductors 196 and 193 toenergize the servomotors 59 and 43 to move the spindle in the requireddirection. As this occurs, spindle movement along the X and Y axesactuates the vector measuring transducers 27 and 28 to provide changingdirection controlling output signal to the circuit. The changing vectormeasurements from the transducers are combined both with fixed pulsesignals from the various pulse dividers activated by the clock generator246, as well as variable pulse signals concomitantly generated byextensible movement of the opposite interferometer. The resultingcontinuously modified X and Y control signals are transmitted from therespective registers and 189 along conductors 195 and 192 for supplyingposition indicating signals to the Y control 178 and the X control 186respectively In FIG. 8 there is illustrated a simplified form of vectormeasuring control system that obviates the necessity for providing onecontroller to continuously square the vector measured distance, and aseparate cooperating controller operative to extract the square root ofa summed input that includes the square of the vector measurement. Aspreviously described in connection with FIG. 7, separate controllers 218and 289 are respectively connected to continuously square the vectormeasurements from counters 212 and 285. In addition, the control systemschematically illustrated in FIG. 7 requires additional controllers 228and 294 respectively operative to extract the square root of theseparately summed inputs for the X and Y positions respectively.

The simplified control system illustrated in FIG. 8 is provided withcertain control elements identical to those illustrated in FIG. 7 andidentified by like reference numerals. For example, the numericalcontrol system 166 is connected to provide command signals via outputconduits 167 and 171 respectively connected to actuate the spindle ratecontrol 169 and the Z axis command register 172. In like manner, priorto and end of block signal, control commands are transmitted byconductors 174 and 182 respectively connected to actuate a Y axiscommand register 175 and an X axis command register 183. Furthermore,the clock oscillator 246 is connected to generate signals for energizingand providing uniform or fixed pulse signals to pulse dividers 235, 254,253 and 243, all of which provide signals of predetermined value andrespectively corresponding to the fixed offsets of the pivot axesdescribed in connection with FIG. A.

The simplified and faster operation of the control circuit illustratedin FIG. 8 is predicated upon the fact that it is possible to directlyadd the increments of the successive square roots of successivelysquared numbers. With vector measurements being effected by laserinterferometers, the value of each pulse for effecting an incrementalchange in position is equal to one light fringe or 6% millionths of aninch. As already explained, the RB counter 212 and the RA counter 285 inFIGS. 7 and 8 are respectively disposed to express the rectilinearmeasurement of the distance between the spindle pivot axis and the G andH pivot axes in terms of total pulses comprising the RA and RB beamsplus the offsets at opposite ends of the beams. As explained in FIG. 7,the total value of RB signal pulses in the counter 212 is incremented ordecremented in accordance with the direction of movement along the Xaxis and the order of phase differentiated input pulses via conductors209 and 210. In a similar manner, the total number of RA signal pulsesin the counter 285 is incremented or decremented in accordance with thedirection of movement along the Y axis. With the position indicatingcounters 212 and 285 thus activated to indicate the respective positionsof movement along the X and Y axes, the control system schematicallyillustrated in FIG. 8 is operative to provide light fringes indicatingpositioning measurements corresponding to the orthogonal movements ofthetool spindle along the X and Y axes.

Instead of perfonning the separate functions of first squaring and thenextracting the square roots of position detennining signals, the controlcircuit illustrated in FIG. 8 is provided with simplified controllersoperative to directly add the incremental differences between successivesummed inputs including successively squared signals. This arrangementsimplifies and greatly accelerates the computational operations requiredto accurately change the vector measurements into orthogonal positioncontrolling feedback measurements. To illustrate the fact that similarcontrollers are utilized in different cooperating portions of the entiresystem, the letter N will be used to illustrate the value of RA, RB, orthese values with offsets such as Y-A (X-B) et cetera.

With these conditions existing, it will be further assumed that:

Thus, if N increases by one pulse of by one unit, then N increases bythe incremental or pulsed value of (2N+l) units.

In a similar manner, with Therefore, if N decreases by one unit or byone pulse, then N decreases by the incremental or pulsed value of (2N+l)units.

These relationships can be further illustrated by the followmg numencalvalues substituted for the letter values as follows:

Incremental difference between N N squared values 7 49 8. 64 15(2X7-l-1) t) 81 17 (2X8+1) l0 19 (2X9+1) 11. 121 21 (2X10+1) l0. 100 21(2X11-1) 9 81 19 (2X10-1) 8. 64 17 (2X9-1 7. 49 15 (2X8-1) s. 36 13(2x7-1) 5 25 11 (2}(6-1) Thus, depending upon the direction of X axismovement, the RB vector measuring counter 212 provides a single 1 outputpulse along a conductor 302 connected to actuate an incremental squaringpulse control 303. As hereinbefore described with reference toincrementing or decrementing the value of N the squaring pulse control303 is operatively disposed to continuously perform the operations of(i2RB+ l as required by the input signal; and, transmits the resultingsignal along a conductor 306 to actuate a summing register 307comprising the (X) error accumulator. In addition to the incrementalsquaring pulse control signal along conductor 306, the summing register307 is connected to receive two other modifying control signals viainput conductors 309 and 310 respectively.

As illustrated in FIG. 8, one modifying signal is provided by an addercontrol 312 which is connected to receive input signals from two sourcesand combine these signals to provide the resulting output signal havinga value of fl(X+A)+l which is transmitted along the conductor 309 to thesumming register 307. In a similar manner, another adder control 314 isconnected to receive input signals from two sources and add thesesignals to provide a resulting signal having a value 12(Y-H-l fortransmission along the conductor 310 to the summing register 307. Theseparate total signal pulses respectively supplied along inputconductors 306, 309 and 310 are combined by the summing register 307which is connected to provide resultant direction indicating outputsignals along output conductors 316 and 317 which are connected toactuate the X position register 189 for indicating the horizontalposition of the tool spindle. Conductors 316 and 317 are respectivelyconnected by conductors 318 and 319 to provi c direction indicating,positional signals to an X axis error counter 322. The X axis errorcounter 322' is connected via conductors 324 and 325 to receive signalsfrom the X axis command register 183 whichis adapted to receive positioncontrolling input commands from the numerical control system 166, ashereinbefore explained. Depending upon the difference between thedirectional indicating positional feedback commands via conductors 318and 319, and the commanded position via conductors 324 and 325, the Xaxis error counter 322 provides a direction controlling error signal viaoutput conductor 327 for actuating the X axis servocontrol 162 tooperate the X axis servomotor 43 for effecting X axis movement to theselected position.

In a similar manner, the RA vector measuring counter 285 provides asignal along a conductor 328 to activate an incremental squaring pulsecontrol 329. Depending upon the vertical direction of movement of thespindle along the Y axis, the squaring pulse control 329 provides anoutput signal having a value -(2RA+l) which is transmitted along aconductor 332 to actuate a summing register 333 which is connected toreceive modifying signals along input conductors 335 and 336. A firstadder control 338 is connected to receive two input signals and combinethe separate inputs to produce a signal having a value i2(X-+C)+l whichis transmitted along the output conductor 335 to provide one modifyinginput signal to the summing register 333. A second adder control 340 islikewise connected to receive two separate input signals and combinethose inputs into a signal having a value of :2( Y+ D)+l which istransmitted along conductor 336 to provide a second modifying Sig italto the summing register 333. The summing register 333 is operativelydisposed to combine the three separate input signals received alongconductors 332, 335 and 336 to produce an output signal along conductors344 and 345 which are connected to actuate the Y axis position register190. In addition, the conductors 344 and 345 are respectively connectedvia conductors 346 and 347 to provide position indicating signals to a Yaxis error counter 350. The Y axis error counter is likewise connectedvia conductors 352 and 353 to receive Y axis numerical command signalsfrom the Y axis command register 175. Consequently, the Y axis errorcounter 350 provides direction controlling output error control signalsalong a conductor 355 to operate the Y axis servocontrol 178 foreffecting directionally controlled movement of the Y axis servomotor 59for moving the spindlehead to the selected position.

To provide the properly coordinated modulating signals to the X summingregister 307 and Y summing register 333, pulsating signals areoriginated by the position registers 189 and 190, as well as the fixedcontrol dividers 235, 243, 253 and 254. The Y position vertical register190 is connected to provide an output signal along conductor 360 toactivate an incremental squaring pulse control 361. The squaring pulsecontrol 361 is provided with a control circuit adapted to receive thepulsating Y position indicating signal from conductor 360 and convertthe value of this signal to :2Y+l that is transmitted along an outputconductor 362 connected to a common line 364. The common line 364 isconnected at its opposite ends to transmit the pulse control signal:2Y+l to the respective adders 314 and 340.

In a similar manner, the X position register 189 is connected totransmit a signal continuously equal to the value of the X position viaa conductor 372 to an incremental squaring pulse control 373. The Xposition signal from the conductor 372 is converted by the squaringpulse control 373 to a value :t2X+1 which, in turn, is transmitted alongan output conductor 376 to a common conductor 377. Thus, the conductor377 is connected to transmit a signal having a value of :tZX-l-l to therespective adders 312 and 338.

To complete the separate modifying signals to the summing register 333,the respective pulse controls 254 and 235 are connected to provide anorigin of fixed or nonvarying signal pulses of predetermined value forthe adders 340 and 338. To accomplish this, the signal pulse input (-D)from the pulse control 254 is connected via conductor 367 to a controlcircuit 368 operative to translate the input signal into a pulsatingsignal having a fixed value of :2D. The resulting signal from thecontrol circuit 368 is transmitted via a conductor 369 to the adder 340where it is combined with the incremental pulse to signal from thecommon input conductor 364. Consequently, the adder 340 provides asignal having a value t2(Y-H-l constituting a variable pulsating signaltransmitted along conductor 336 to the summing register 333. In asimilar manner, the pulse control 235 is connected to transmit a fixedpulse output signal having a value of (-C) light fringes via a conductor380 to a control circuit 381. The control circuit 381 is operative toconvert the fixed pulse (-C) signal to a fixed pulse signal having avalue of :tZC which is transmitted along conductor 382 to the adder 338for combining with the variable pulse signals supplied thereto along theconductor 377. The control circuit within the adder 338 is operative toconvert the fixed and variable pulse signals supplied thereto into avariable signal having a value -2(X+C)+l transmitted along conductor 335to the summing register 333. As hereinbefore explained. the summingregister 333 is operative to combine the input signals transmittedthereto along conductors 332. 335 and 336 to provide the Y axis errorcontrol signals along output conductors 344 and 345.

In a similar manner, the pulse controls 243 and 253 operate as a sourceof fixed pulse signals for the adders 312 and 314 respectively. From thepulse control 243, a fixed pulse signal having a (-A) value istransmitted along conductor 385 to a cont 386 that is era damsel}?!qnyst t i rm signal to a flA value. The resulting flA signal from thecontrol 386 is transmitted along conductor 387 to the adder 312 whichoperates to combine the fixed input signal with a variable pulse signalfrom the conductor 377. The adder 312 is thus operative to provide acombined output signal having a value :2(X-H-l for transmission alongthe conductor 309 to the summing register 307. At the same time, thepulse control 253 provides a fixed pulse signal output (-8) alongconductor 390 to a control 391 adapted to convert the fixed input signalto a signal having a :2:2B value. From the control 391, the t 28 fixedpulse signal is transmitted along conductor 392 to the adder 314 forcombining with the variable pulsed input signal supplied thereto via theconductor 364. The adder 314 operates to provide a fixed pulse signalhaving a value of 12(Y-H-1 along the output conductor 310 to the summingregister 307. As hereinbefore explained, the summing register 307operates to combine the three separate input signals respectivelytransmitted thereto via conductors 306, 309 and 310 to provide anaccurate X axis position indicating signal along output conductors 316and 317.

From the foregoing description of the circuit diagrammaticallyillustrated in FIG. 8, it will be apparent that a greatly improvedarrangement has been provided for simplifying the square and square rootprocess. To accomplish this, a simplified circuit is arranged to workdirectly on small differences between the numbers to be squared, or fromwhich the square root is to be extracted. Actually, the circuitillustrated in FIG. 8 completely obviates the functions of extractingthe square root and greatly increases the computational speed ofoperation. The block diagram in FIG. 8 operates in a manner to diminishthe X position if QA exceeds 0 and to increase the X position if QA isnegative. In a similar manner, the Y position is increased or decreasedby one unit (pulse or fringe) at a time in order to adjust QB as closeto 0 as possible. Inasmuch as both of these equations are being adjustedcontinuously and affect one another, the computations must take placequickly with the resulting values of the X and Y positions beingcontinuously available to supply the required feedback information forcomparison with X and Y commands from the tape.

It is preferable that the vector measuring interferometers 27 and 28,FIG. 1, be reasonably close to a perpendicular relationship to oneanother. However, the degree of perpendicular relationship willobviously change during operation. For example, leftward and downwardmovement of the spindle 'tead 48 from the position shown in FlG. 1 willincrease the perpendicular relationship between the vector measuringinter ferometers 27 and 28. Maintaining a reasonably close perpendicularrelationship between the interferometers improves the degree ofresolution as movement is effected.

To facilitate the description, as shown in FIG. 1, the vector measuringtransducers 27 and 28 have been illustrated as beingin predeterminedangular relationship to one another as well as to the perpendicular Xand Y axes of movement of the tool support. In similar manner, as shownin FIGS. 5 and 7, the vector measuring beams RA and RB are schematicallyillustrated as being in similar predetermined angular relationshipbetween the common spindle pivot axes and the angularly spaced apartpivot axes G and H of the frame or base 21. It is emphasized that theparticular angular vector relationships shown and described areillustrative only and have been selected to facilitate and simplifyexplaining the invention.

It is further emphasized that in a preferred embodiment of theinvention, the vector measuring transducers are maintained as nearly aspossible perpendicular to one another as

1. In a machine tool having a positioning control system; a frame; afirst member carried by said frame for selective rectilinear movementtherealong; a second member movably carried by said first member forselective movement along an axis perpendicular to the axis of movementof said first member; a pair of rectilineal measuring transducerspivotally interconnected between said second member and spaced-apartportions s of said frame for respectively measuring the distance betweensaid second member and spaced apart portions of said frame; separatetriangulation position measuring means simultaneously responsive to saidtransducers for respectively indicating the positional movement of saidfirst member along said frame and the perpendicular movement of saidsecond member along said first member; and separate power translatorsrespectively interconnected between said frame and said first member aswell as between said first member and said second member; saidtranslators respectively connected to be coordinately actuated by saidseparate triangulation measuring means.
 2. In a machine tool accordingto claim 1 in which said measuring transducers comprise separate andindividually extensible laser interferometers respectively adapted tomeasure the distance between said second member and said frame.
 3. In amachine tool according to claim 1, including separate telescopingtubular supports respectively operative to protect and guidablyconstrain said respective transducers during measuring movement.
 4. In amachine tool having a frame; a rotatable tool spindle movably guided bysaid frame for rectilinear movement in mutually perpendicular planes,each perpendicular to the rotational axis of said spindle; a first and asecond power drive respectively connected to effect selective movementof said spindle along its perpendicular axes of movement; a first and asecond lineal transducer each pivotally connected at its inner end tosaid spindle and extending outwardly in angularly diverging directionsin a plane perpendicular to the axis of said spindle, said transducersbeing pivotally secured at their opposite outer ends to spaced apartportions of said frame; a fIrst and a second counter respectivelyconnected to be actuated by said first and second transducers toindicate the respective rectilinear angular positions of said spindlerelative to said frame; a first and a second accumulator respectivelyactuated by said first and second counters operative to provide outputfeedback control signals respectively representing the separateperpendicular axes of movement; a first modulator connected to transmitsignals from said second accumulator to predeterminately modify thefeedback signals from said first accumulator; a second modulatorconnected to transmit signals from said first accumulator topredeterminately modify the positional feedback signals from said secondaccumulator; and, a numerical control system adapted to selectivelyactuate said power drives for effecting corresponding positionallycontrolled movement of said tool support along its perpendicular pathsof movement to predetermined positions as determined by the respectivelymodulated perpendicular feedback control signals from said first andsecond accumulators.
 5. In a machine tool having a rotatable toolsupport carried for rectilinear movement in mutually perpendicularplanes; a frame disposed to guide said tool support for selectiverectilinear movement in perpendicular planes both perpendicular to therotational axis of said tool support; power drives respectively operableto selectively move said tool support along its perpendicular paths ofmovement; a pair of separate lineal measuring transducers each pivotallyconnected at one end to said tool support and each extending inangularly diverging directions and in planes perpendicular to the axisthereof, said transducers extending from said tool support in angulardirections relative to the perpendicular paths of movement thereof andbeing pivotally secured at their opposite outer ends to spaced apartportions of said frame; a pair of separate counters respectivelyconnected to be activated by said transducers for respectivelyindicating angular increments of change in the lineal distance measuredby each of said transducers upon movement of said tool support inresponse to either of said power drives; a pair of separate squaringcontrols respectively connected to be actuated by said counters forproviding output control signals; a first and a second accumulatorresponsive to output signals from said squaring controls; a firstcontrol actuated by one of said accumulators and connected to said firstpower drive for moving said tool support along one axis; firstmodulating means connected to transmit signals from said secondaccumulator to predeterminately modify the input signals to said firstaccumulator and said first control actuated thereby; a second controlactuated by said second accumulator and connected to said second powerdrive for moving said tool support along the other perpendicular axis;and, second modulating means connected to transmit signals from saidfirst signal accumulator to predeterminately modify the input signals tosaid second accumulator and said second control actuated thereby.
 6. Ina machine having a frame; a support member guided by said frame forselective relative movement along first and second orthogonal axes;first and second transducers pivotally interconnected between a commonpivot on said support member and a pair of spaced apart pivots on saidframe; power drive means connected to move said support member along aselected one or both of said orthogonal axes; a first controllerresponsive to coordinate combinations of signals from both of saidtransducers for providing a first positional signal to indicateorthogonal positional movement of said support member along said firstaxis and; a second controller responsive to different combinations ofsignals from both of said transducers for providing a second positionalsignal to indicate coordinate positional movement of said sUpport memberalong said second transverse axis.
 7. In a machine according to claim 6in which said first and second transducers respectively compriseindividually extensible laser interferometers.
 8. In a machine toolhaving: a frame; a tool support movably guided by said frame forselective movement along perpendicular axes; first and second powerdrives respectively operable to move said tool support in a selected oneof its perpendicular axes of movement; a first and second linealtransducer each pivotally connected at one end to said tool support anddisposed to extend in angularly diverging directions for pivotalconnection at their outer ends to spaced apart portions of said frame; afirst and second signal accumulator respectively connected to beactuated by said first and second transducers for measuring the angulardistances between said tool support and the respectively spaced apartportions of said frame; a first modulator connected to transmit signalsfrom said second accumulator to predeterminately modify said firstaccumulator for rendering a feedback signal therefrom indicative of therectilinear position of said tool support along said first perpendicularaxis; a second signal modulator connected to transmit signals from saidfirst accumulator to predeterminately modify said second accumulator forrendering a feedback signal therefrom indicative of the rectilinearposition of said tool support along said second perpendicular axis; and,a numerical control system operative to effect selective actuation ofsaid first and second power drives for moving said tool support to aselected position along said first and second axes as determined bymodulated feedback signals from said first and second signalaccumulators.
 9. In a machine having a frame presenting a pair of spacedapart parallel pivots; a first member guided by said frame forrectilinear movement along a first axis; a second member guided by saidfirst member for rectilinear movement along a second axis perpendicularto said first axis; a tool receiving support carried by said secondmember presenting a common pivot parallel to said spaced apart pivotspresented by said frame; a first and second measuring transducer eachpivotally connected at one end to said common pivot and extending indiverging angular directions relative to said first and second axes forrespective pivotal connection at their opposite ends to said spacedapart pivots presented by said frame; power drive means selectivelyoperable to move said first member along said first axis and said secondmember along said second axis for moving said tool support to a selectedposition relative to said frame; a first controller connected to besimultaneously actuated by a position signal from said first transducerand a predetermined modulating signal from said second transducer in amanner to produce a single first feedback signal for controllingposition along said first axis; a second controller connected to besimultaneously actuated by a principal signal from said secondtransducer and a predetermined modulating signal from said firsttransducer in a manner to produce a single second feedback signal forcontrolling position along said second axis; and, a data control systemconnected to effect positionally controlled operation of said powerdrive means for effecting positionally controlled movement of said toolsupport according to predetermined positional feedback signals from saidfirst and second controllers.
 10. In a machine tool having a supportframe; a first member movably carried by said frame for rectilinearmovement along a first axis; a second member movably carried by saidfirst member for rectilinear movement along a second axis perpendicularto the first axis of movement; a tool support carried by said secondmember and extending in a direction perpendicular to the axes ofmovement of said first and second members; A first interferometerpivotally connected at one end to said tool support and pivotallyconnected at its opposite end to a first portion of said frame; a secondinterferometer pivotally connected at one end to said tool support andpivotally connected at its opposite end to a portion of said framespaced from said first portion of said frame; first and second powerdrives respectively connected to move said first and second members intheir respective perpendicularly disposed axes of movement forpositioning said tool support; first and second position controllersrespectively connected to receive signal pulses from said respectiveangularly disposed first and second interferometers during movement ofsaid tool support in either perpendicular axis of movement; a firstmodulator connected to transmit predetermined signal pulses from saidsecond controller to said first controller for so combining with theangular position pulses transmitted thereto as to provide uniformpositional control signals for indicating rectilinear movement of saidtool support along said first axis; a second modulator connected totransmit predetermined signal pulses from said first controller to saidsecond controller for so combining with the angular position pulsestransmitted thereto as to provide uniform positional control signals forindicating rectilinear movement of said tool support along said secondaxis; and, a numerical control system connected to effect selectiveactuation of said power drives for moving said first and second membersto predetermined positions along their respective perpendicular aces ofmovement as determined by positional control signals from said first andsecond position controllers.
 11. In a machine tool having: a frame; afirst member slidably carried thereby for rectilinear movement along oneaxis; a second member slidably carried by said first member forrectilinear movement along a perpendicular axis; a tool support carriedby said second member and extending in a direction perpendicular to themutually perpendicular axes of member movement; separate servodrivesrespectively connected to move said first and second members along theirperpendicular axes of movement; a numerical control system operative toactuate said servodrives for moving said tool support along its selectedperpendicular axes of movement relative to said frame; first and secondrectilinear transducers pivotally connected at one end to said toolsupport and extending therefrom in angularly diverging directions, saidtransducers being pivotally secured at their opposite outer ends tospaced apart portions of said frame; first and second signalaccumulators respectively actuated by said first and second transducersupon movement of said tool support along either of its perpendicularaxes of movement; first modulating means connected to transmit signalsfrom said second accumulator to predeterminately modify the signaloutput from said first accumulator to indicate the proportionalincremental movement of said tool support along said first axis; secondmodulating means connected to transmit signals from said firstaccumulator to predeterminately modify the transducer signal input tosaid second accumulator to indicate the proportional incrementalmovement of said tool support along said second perpendicular axis; and,a numerical control system connected to effect predetermined actuationof said first and second servo servodrives for controlling perpendicularmovement of said tool support to selected positions along said first andsecond perpendicular axes as determined by modulated positional feedbacksignals from said first and second accumulators.
 12. In a machine toolhaving: a frame; a tool support guided by said frame for rectilinearmovement in first and second mutually transverse axes; power drive meansoperative to effect movement of said tool support along a selected axis;a pair of posItion measuring transducers each pivotally connected at oneend to said tool support and each pivotally connected at their oppositeends to spaced apart portions of said frame; a first and secondmeasuring control respectively responsive to said transducers formeasuring the angular distances between said tool support and saidspaced apart portions of said frame; a first modulator means connectedto combine predetermined signals from said second control with the inputto said first control for producing a uniform first rectilinearmeasurement parallel to said first rectilinear axis of movement of saidtool support; second modulating means connected to combine predeterminedsignals from said first control with the input to said second controlfor rendering said second control operable to provide a combinedrectilinear measurement signal parallel to said second axis of movementof said tool support; and, a numerical control system operative toprovide command data for actuating said power drive means to effectselective rectilinear movement of said tool support along a selectedaxis as determined by each of the combined positional indicatingfeedback signals from said first and second measuring controlsrespectively.
 13. In a machine tool having: a frame; a tool supportguidably carried by said frame for selective rectilinear movement alongmutually perpendicular axes; first and second transducers beingrespectively and pivotally connected at their outer ends to spaced apartpivot axes presented by said frame and at their inner ends to a commonpivot axis carried by said tool support; first and second power drivesconnected to effect selective movement of said tool support along eachperpendicular axis of movement a first controller responsive topredeterminately proportioned signals from said transducers forproducing feedback signals adapted to control movement of said toolsupport along its first axis of movement; a second controller responsiveto predeterminately proportioned signals from said transducers forproducing feedback signals adapted to control movement of said toolsupport along its second perpendicular axis of movement; and, apositional control system operative to effect coordinate control of saidpower drives for moving said tool support to a selected position asdetermined by preselected feedback error control signals from saidcontrollers.
 14. In a machine tool according to claim 13 wherein saidfirst and second transducers respectively comprise first and secondlaser interferometers.
 15. In a machine tool having a base and a columnslidably carried by said base; a spindlehead slidably carried by saidcolumn for movement along an axis perpendicular to the axis of columnmovement; first and second servo-driven translators respectivelyconnected to selectively move said column and said spindlehead; anumerical control system connected to selectively move said translators;a spindle journaled in said spindle head for rotation about an axisperpendicular to the axes of head and column movement; a firsttransducer pivotally connected at one end to said tool spindle and atits opposite end to said base; a second transducer pivotally connectedat one end to said tool spindle and at its opposite end pivotallyconnected to a spaced apart portion of said base; first triangulationmeasuring means actuated by said transducers during movement of saidspindle relative to said base to provide a first signal for indicatingthe positional movement of said column along said base; secondtriangulation measuring means actuated by said transducers during bodilymovement of said spindle relative to said base to provide a secondsignal for indicating the positional movement of said spindlehead alongsaid column; first feedback control means providing an error signal toactuate said first servo translator comprising the difference betweenpositional command signals from saiD numerical control system and saidfirst triangulation measuring means; and, second feedback control meansproviding an error signal to actuate said second servo translatorcomprising the difference between positional command signals from saidnumerical control system and said second triangulation measuring means.16. In a machine tool, a pair of members carried for relative movementalong perpendicular axes; separate power translators connected to effectrectilinear movement of said members along said respective axes; acommon pivot carried by one of said members relative to a pair of spacedapart pivots carried by the other of said members; a pair of extensiblerectilinear measuring transducers pivotally secured at one end to saidcommon pivot and extending in angularly diverging directions, saidmeasuring transducers being pivotally secured at their opposite outerends to said spaced apart pivots; first triangulation measuring meansresponsive to rectilinear measuring signals from said transducersconnected to indicate relative positional movement between said membersalong one axis of movement and, second triangulation measuring meansresponsive to rectilinear measuring signals from said transducersconnected to indicate relative positional movement between said membersalong the other perpendicular axis of movement.